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Explore collective motion phenomena through the lens of congestion principles in this comprehensive lecture by Bertrand Maury from LMO at Institut des Hautes Etudes Scientifiques. Examine how interactions in collective systems primarily stem from congestion rather than traditional swarming or collaborative behaviors, focusing on crowd motion models where individual tendencies are counteracted by the presence of others. Investigate the propagation of information through populations and delve into gradient flow type models that assume populations minimize global dissatisfaction while incorporating congestion constraints. Learn about microscopic approaches to this framework alongside macroscopic extensions based on Optimal Transportation principles, understanding how classical mechanics principles including Action-and-Reaction symmetric interactions can be modified to create more realistic interaction models with asymmetric individual interactions. Discover how mathematical modeling can capture the complex dynamics of collective motion systems where congestion plays the dominant role in shaping group behavior.
